Archive for July, 2012

A Hypercube by any other name

Wednesday, July 4th, 2012

Hypercube loudspeaker

Hypercube loudspeaker

Sometimes it’s difficult to see something sitting in plain sight.

This is because there are so many ways of looking at things. Johannes Kepler saw it as an inside-out cube. Geologists saw it as lodestone, garnet, copper, lapis lazuli.

Beekeepers saw it as an efficient use of wax and space. But their honey drawers preserved only the two-dimensional aspect of the lattice — the hexagonal grid.

Rhombic Dodecahedron

Rhombic Dodecahedron

Mathematicians saw it as a minor non-Platonic solid — an alternative form of the dodecahedron.

But we know differently. We see differently. We see that the rhombic Dodecahedron (so-called) is actually the outer envelope of one of the projections of the 4D hypercube onto 3-space.

Shakespeare might have said that that which we call a hypercube, by any other name would smell as sweet. But there is something in a name if you want to get attention. Calling this shape “one of the crystalline forms of garnet” misses the point and relegates it to obscurity.

tesseract loudspeaker

tesseract loudspeaker

Perhaps ancient describers were trapped by their 3-dimensional outlook. The Hypercube is best appreciated not as a static form but as a geometry embedded in four-dimensional spacetime. This would seem obvious in retrospect, but was not fully realized until the advent of the audio industry at the beginning of the 20th century. For the first time moving 4-dimensional sound wavefronts were being produced under controlled conditions.

When we regard the rhombic dodecahedron as a geometry embedded in spacetime affecting the propagation and movement of energy in spacetime, then we begin to see more of its possibilities.

The rhombic dodecahedron form of the hypercube excels as a wave trap. In the Middle Ages people believed that a pentagram could somehow trap a demon. Nowadays we see quantum dots trapping electrons. The RD can support cube-shaped standing waves at a wide spectrum of frequencies. Since the tapering pyramidal points crowd sound waves into turning around without hitting a solid wall, this geometry supports resonance across the spectrum. The favoritism of old-style speaker cabinets that boomed some notes and stifled others is now obsolete forever. This harnessed resonance is a result simply of altering the boundary geometry of the air inside the speaker cabinet.

It is no accident that the “rhombic dodecahedron” turns out to have acoustic advantages as a resonator; changing the shape changes the boundary, which changes the air flow, which changes the performance.
—MRK

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More Craning

Tuesday, July 3rd, 2012

cranes across the neighbors driveway

cranes across the neighbor's driveway

More Sandhill cranes strolling through the neighborhood. I captured these with my 5MP digital camera as they had just crossed our neighbor’s driveway moving away from us. I left in the driveway for scale so you can get an idea how big these birds are — almost 4 feet tall !

closeup of cranes

closeup of cranes




Here is a closer look
(click to enlarge).


The sandhill cranes do not have the white feathers of the whooping cranes; you can see their feathers are, instead, a sort of camo randoming of browns.

closeup2 of cranes

closeup2 of cranes



The first two images showed them in a “two hanging out + one ‘distracted’ ” grouping. Here they became aware of me and all three are moving off together in a 3-grouping.

—MRK

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